# Pendulum

## A simple pendulum oscillates in the vertical plane due to gravity

A simple - or mathematical - pendulum consists of a rigid body suspended from a fixed horizontal axis about which the body may oscillate in a vertical plane due to the action of gravity.

The oscillating period for a simple pendulum can be calculated as

*T = 2 π (l / a _{g})^{1/2} (1)*

*where *

*T = oscillating period for one cycle (s)*

*l = length of the pendulum (m, ft)*

*a _{g} = acceleration of gravity (9.81 m/s^{2}, 32.17 ft/s^{2})*

### Example - Calculate the length of a pendulum with an oscillating period of *1 sec, 10 sec and 100 sec*

The length of a pendulum with a given oscillating period can be calculated by transforming *(1)* to:

*l = (T / (2 π)) ^{2} a_{g}*

Length for *1 sec* - typically for an old fashion pendulum clock:

*l = ((1 s) / (2 π)) ^{2 }(9.81 m/s^{2})*

* = 0.249 (m)*

Pendulum clocks were the world standard for accurate timekeeping for 270 years until the quartz clock was invented in 1927.

Length for *10 sec*:

*l = ((10 s) / (2 π)) ^{2 }(9.81 m/s^{2})*

* = 24.9 (m)*

Length for *100 sec*:

*l = ((100 s) / (2 π)) ^{2 }(9.81 m/s^{2})*

* = 2487 (m)*

### Four Types Of Pendulums

It is common to differentiate between four types of pendulums:

**Compound or Physical Pendulum**- A rigid body suspended from a fixed horizontal axis. The body may oscillate in a vertical plane due to the action of gravity.**Simple or Mathematical Pendulum**- Similar to the compound or physical pendulum but the mass is concentrated in a single point and oscillates back and forth in the vertical plane. The mass point is connected to a horizontal axis with a weightless chord.**Conical Pendulum**- Similar to the simple pendulum except that the weight suspended by the chord moves in uniform speed around the circumference of a circle in the horizontal plane.**Torsional Pendulum**- A disk fixed to a slender rod. The rod is fastened to a fixed frame. If the disk is twisted it will oscillate back and forth about the axis of the rod.